Turbulent flow past a smooth and rigid wall-mounted hemisphere

Semi-confined flows

Underlying Flow Regime 3-33

Evaluation

Unsteady results

Based on the experimental and numerical unsteady data the flow field is characterized using the systematic classification map of the unsteady flow patterns given by Savory and Toy (1986) (see Fig. 1). Seven regions are highlighted:

(1) Upstream the hemisphere the horseshoe vortex system dominates. The hemispherical bluff body acts as a barrier, leads to positive pressure gradient, so that the boundary layer separates from the ground forming this the horseshoe vortex system.

(2) The stagnation area is located close to the lower front surface of the hemisphere, where the stagnation point is found at the surface at an angle of about $\theta _{\text{stag}}^{\text{LDA}}\approx 166^{\circ }$ (definition of $\theta$ in Fig. 1).

(3) Then, the flow is accelerated along the hemisphere. Therfore, it is called the acceleration area. It results to a high level of vorticity near the hemispherical surface.

(4) At an angle of $\theta _{\text{sep}}^{\text{LDA}}\approx 90^{\circ }$ the flow detaches along a separation line.

(5) As a consequence of the flow separation a recirculation area appears and is cut from the outer field by a dividing line.

(6) Strong shear layer vorticity can be observed leading to the production of Kelvin-Helmholtz vortices which travel downstream in the flow field.

(7) To close the recirculation area the flow reattaches at the reattachment point. In this region the splatting effect occurs, redistributing momentum from the wall-normal direction to the streamwise and spanwise directions.

Fig. 1: Visualization of flow regions and characteristic flow features of the flow past the hemisphere: (1) horseshoe vortex system, (2) stagnation area, (3) acceleration of the flow, (4) separation point, (5) dividing streamline, (6) shear layer vorticity, (7) reattachment point.

The 3D geometry generates a 3D flow field illustrated in Fig. 2. The complex flow pattern are visualized using iso-surfaces of the pressure fluctuations ( $p'/(\rho _{\text{air}}U_{\infty }^{2})=-2.47\times 10^{-4}$ ) as recommended by Garcia-Villalba et al. (2009):

Just upstream the bluff body the horseshoe vortex system dominates and leads to necklace-vortices that stretch out on both sides into the wake region.

After detaching along the separation line the flow rolls up.

In the wake these small roll-up vortices interact together and/or with the horseshoe vortices conducting to the formation of big entangled vortical hairpin-structures. These pattern travel downtream forming a vortex chain. Schematic 3D sketches and explanations of the formation of the hairpin-structures around and behind the hemisphere can be found in the literature (Tamai et al., 1987, Acarlar and Smith, 1987).

Fig. 2: Snapshot of unsteady vortical structures visualized by utilizing the iso-surfaces of the pressure fluctuations ( $p'/(\rho _{\text{air}}U_{\infty }^{2})=-2.47\times 10^{-4}$ ) colored by the spanwise instantaneous velocity.